Showing papers by "Ernest R. Davidson published in 1976"

The two lowest energy 2A′ states of NO2

Abstract: The 2A1 ground state of NO2 and the so‐called 2B2 excited state are shown to form a strongly coupled pair of 2A′ states when asymmetric distortion is considered. This coupling is of the Jahn–Teller type although the degeneracy between the states is accidental and the normal coordinates are not equivalent.

An ab initio potential‐energy surface study of several electronic states of NO2

Abstract: The results of ab initio potential‐energy surface calculations are presented for 12 doublet and four quartet states of NO2. In several cases Cs as well as C2v conformations have been studied. The predicted equilibrium conformations and the character of the wavefunctions are discussed. Vertical excitation energies are given for 40 doublet and 12 quartet states. The electronic spectrum of NO2 is discussed, and barriers to photodissociation are estimated for several electronic states. Whether states will be strongly Jahn–Teller coupled by a symmetry‐reducing vibrational interaction depends on their potential surfaces and the character of their wavefunctions. This vibronic interaction in some cases is expected to produce non‐C2v equilibrium conformations.

An SCF method for hole states

Abstract: An SCF method is derived for doublet states with one vacancy in an orbital within the occupied manifold (hole states). This method gives an upper bound to an excited state energy. Hence it is a stable procedure which is bounded from below and cannot collapse to a lower energy SCF state. This new procedure is compared with several other open‐shell SCF procedures which have been advocated for the ground doublet state.

Abinitio evaluation of the fine structure and radiative lifetime of the 3A2(n→π*) state of formaldehyde

Abstract: The spin–orbit contribution to the zero‐field splitting (ZFS) in the CH2O 3 A 2(n→π*) state is evaluated using the full Breit–Pauli Hamiltonian. All calculations are carried out at the planar ground state geometry using a double‐zeta plus polarization basis of contracted Gaussian‐lobe functions augmented with diffuse s and p functions. Configuration–interaction wavefunctions, constructed using the 3 A 2 canonical orbitals, are used to describe the 3 A 2 state and all states coupling to it via the spin–orbit Hamiltonian. The excitation energies and oscillator strengths obtained from these wavefunctions are in good agreement with other theoretical calculations and with experiment. Of the 12 states considered in the second‐order perturbation theorytreatment of the spin–orbit interaction, the 1 A 1 ground and the nearby 3 A 1(π→π*) states were the most important. Rydberg states were observed to have very small spin–orbit matrix elements and consequently to have little effect on the ZFS. The spin–orbit contributions to the ZFS parameters D and E were −0.224 and 0.009 cm−1, respectively, which when added to the spin–spin contribution obtained in an earlier paper [S. R. Langhoff, S. T. Elbert, E. R. Davidson, Int. J. Quantum Chem. 7, 999 (1973)] give total values of D=0.314 cm−1 and E=0.04 cm−1. These results are larger than the best experimental results of D=0.141 cm−1 and E=0.02 cm−1, determined by Birss e t a l. [F. W. Birss, R. Y. Dong, and D. A. Ramsay, Chem. Phys. Lett. 18, 11 (1973)] from a rotational analysis of the 0+←0 bands of the 3 A 2←1 A 1 transition. An extensive calculation was also undertaken to assess the degree of convergence in the second‐order perturbation theorytreatment. The contribution of the lowest 100 singlet and triplet states of A 1, B 1, and B 2 symmetry were considered where each state was described by a 100‐term CI wavefunction. This calculation gives a spin–orbit contribution to D of −0.221 cm−1 essentially identical to the previous result providing evidence that the second‐order treatment has indeed converged. The radiative lifetimes of the three sublevels of the triplet state were determined using the same representations for the manifold of electronic states. In the high temperature limit, the radiative lifetime was determined to be between 0.02 and 0.06 sec, somewhat longer than the estimated experimental value of 0.01 sec. The mutual perturbation of the 1 A 1 ground and 3 A 2 states and the perturbation of the 3 A 2 state by the 1 A 1(π→π*) state were determined to be most important in determining the lifetime. These results ensure that the emitted light is polarized primarily along the carbon–oxygen bond in agreement with experiment. A critical examination of the quantitative validity of the numerical results is presented to assess the reliability of the theoretically determined lifetimes.

Multicomponent analysis in clinical chemistry by use of rapid scanning fluorescence spectroscopy.

Abstract: To be useful in the clinical laboratory, multicomponent fluorescence analysis requires both the rapid measurement of the fluorescence intensity at a variety of excitation and emission wavelengths and the unambiguous reduction of the data by efficient algorithms. The Video Fluorometer, which exploits the multi-channel capability of a low-light-level television sensor to simultaneously acquire excitation and emission spectra, can meet the first requirement. For example, a complete set of emission and excitation spectra for perylene can be obtained in less than 2 s at concentrations of 10(-10) mol/liter. To meet the second need, we present two types of data-reduction strategies: (a)a least-squares fit to the data, with use of the spectra of previously determined compounds likely to be present; and (b)a determination of the eigenvalues and eigenvectors fo the fluorescence matrix, from which the number of components and the possible spectra of each can be estimated. Computer simulations of the least-squares fitting algorithms show that five strongly overlapping components can be determined in the presence of noise with an accuracy of better than 5%. Also, a fluorescent sample containing two species with very similar but unknown spectral properties can be resolved to obtain the spectrum of each.

Configuration interaction calculations for 1E′ trimethylenemethane

Abstract: Complete pi‐space CI calculations have been performed for the 1E′ state of trimethylenemethane in a planar D3h conformation using an STO‐3G basis. Molecular orbitals were defined by SCF calculations with C2v symmetry constraints for the lowest 3B2 and 1B2 states. As expected, the 3B2 orbitals had nearly D3h symmetry while the 1B2 pi orbitals were severely distorted. Full pi‐space configuration interaction calculations for both components of the 1E′ state using each set of molecular orbitals gave four nearly identical energies. This verified that the sigma cores from the two SCF calculations were essentially identical. The 1B2 component of the 1E′ wavefunction resembles an allyl radical plus an electron in a p orbital localized on one methylene group. Hence rotation of this methylene group into a plane orthogonal to the allyl radical should produce only a small change in energy.